共查询到20条相似文献,搜索用时 171 毫秒
1.
Shijun Liao Eugen Magyari 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(5):777-792
The boundary value problem for the similar stream function f = f(η;λ) of the Cheng–Minkowycz free convection flow over a vertical plate with a power law temperature distribution Tw(x) = T∞ + Axλ in a porous medium is revisited. It is shown that in the λ-range − 1/2 < λ < 0 , the well known exponentially decaying
“first branch” solutions for the velocity and temperature fields are not some isolated solutions as one has believed until
now, but limiting cases of families of algebraically decaying multiple solutions. For these multiple solutions well converging
analytical series expressions are given. This result yields a bridging to the historical quarreling concerning the feasibility
of exponentially and algebraically decaying boundary layers. Owing to a mathematical analogy, our results also hold for the
similar boundary layer flows induced by continuous surfaces stretched in viscous fluids with power-law velocities uw(x)∼ xλ.
(Received: June 7, 2005) 相似文献
2.
Evangelos A. Latos Dimitrios E. Tzanetis 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(2):137-151
We investigate the behaviour of solution u = u(x, t; λ) at λ = λ* for the non-local porous medium equation ${u_t = (u^n)_{xx} + {\lambda}f(u)/({\int_{-1}^1} f(u){\rm d}x)^2}We investigate the behaviour of solution u = u(x, t; λ) at λ = λ* for the non-local porous medium equation ut = (un)xx + lf(u)/(ò-11 f(u)dx)2{u_t = (u^n)_{xx} + {\lambda}f(u)/({\int_{-1}^1} f(u){\rm d}x)^2} with Dirichlet boundary conditions and positive initial data. The function f satisfies: f(s),−f ′ (s) > 0 for s ≥ 0 and s
n-1
f(s) is integrable at infinity. Due to the conditions on f, there exists a critical value of parameter λ, say λ*, such that for λ > λ* the solution u = u(x, t; λ) blows up globally in finite time, while for λ ≥ λ* the corresponding steady-state problem does not have any solution.
For 0 < λ < λ* there exists a unique steady-state solution w = w(x; λ) while u = u(x, t; λ) is global in time and converges to w as t → ∞. Here we show the global grow-up of critical solution u* = u(x, t; λ*) (u* (x, t) → ∞, as t → ∞ for all x ? (-1,1){x\in(-1,1)}. 相似文献
3.
4.
Extremal probabilities for Gaussian quadratic forms 总被引:1,自引:0,他引:1
Denote by Q an arbitrary positive semidefinite quadratic form in centered Gaussian random variables such that E(Q)=1. We prove that for an arbitrary x>0, inf
Q
P(Q≤x)=P(χ2
n
/n≤x), where χ
n
2
is a chi-square distributed rv with n=n(x) degrees of freedom, n(x) is a non-increasing function of x, n=1 iff x>x(1)=1.5364…, n=2 iff x[x(2),x(1)], where x(2)=1.2989…, etc., n(x)≤rank(Q). A similar statement is not true for the supremum: if 1<x<2 and Z
1
,Z
2
are independent standard Gaussian rv's, then sup0≤λ≤1/2
P{λZ
1
2
+(1−λ)Z
2
2
≤x} is taken not at λ=0 or at λ=1/2 but at 0<λ=λ(x)<1/2, where λ(x) is a continuous, increasing function from λ(1)=0 to λ(2)=1/2, e.g. λ(1.5)=.15…. Applications of our theorems include asymptotic
quantiles of U and V-statistics, signal detection, and stochastic orderings of integrals of squared Gaussian processes.
Received: 24 June 2002 / Revised version: 26 January 2003
Published online: 15 April 2003
Research supported by NSA Grant MDA904-02-1-0091
Mathematics Subject Classification (2000): Primary 60E15, 60G15; Secondary 62G10 相似文献
5.
Onur Yavuz 《Integral Equations and Operator Theory》2010,68(4):473-485
We consider a multiply connected domain Ω which is obtained by removing n closed disks which are centered at λ
j
with radius r
j
for j = 1, . . . , n from the unit disk. We assume that T is a bounded linear operator on a separable reflexive Banach space whose spectrum contains ∂Ω and does not contain the points
λ1, λ2, . . . , λ
n
, and the operators T and r
j
(T − λ
j
I)−1 are polynomially bounded. Then either T has a nontrivial hyperinvariant subspace or the WOT-closure of the algebra {f(T) : f is a rational function with poles off [`(W)]{\overline\Omega}} is reflexive. 相似文献
6.
Marcelo Montenegro Olivâine S. de Queiroz Eduardo V. Teixeira 《Mathematische Annalen》2011,351(1):215-250
We establish existence and sharp regularity results for solutions to singular elliptic equations of the order u
−β
, 0 < β < 1, with gradient dependence and involving a forcing term λ f(x, u). Our approach is based on a singularly perturbed technique. We show that if the forcing parameter λ > 0 is large enough,
our solution is positive. For λ small solutions vanish on a nontrivial set and therefore they exhibit free boundaries. We
also establish regularity results for the free boundary and study the asymptotic behavior of the problem as
b\searrow 0{\beta\searrow 0} and
b\nearrow 1{\beta\nearrow 1}. In the former, we show that our solutions u
β
converge to a C
1,1 function which is a solution to an obstacle type problem. When
b\nearrow 1{\beta\nearrow 1} we recover the Alt-Caffarelli theory. 相似文献
7.
Here proposed are certain asympotic expansion formulas for L
n
(∞-1)
(λz) and C
n
(∞)
(λz) in which 0<w=0(λ) and Cn/(w)(λz), z being a complex number. Also presented are certain estimates for the remainders (error bounds) of the asymptotic
expansions within the regions D1(-∞<Rez<=1/2(ω/λ) and D2(1/2(ω/λ)<=Rez<∞), respectively.
Supported by NSERC (Canada) and also by the National Natural Science Foundation of China. 相似文献
8.
《偏微分方程通讯》2013,38(7-8):1127-1148
Abstract In this work we analyze the existence of solutions that blow-up in finite time for a reaction–diffusion equation u t ? Δu = f(x, u) in a smooth domain Ω with nonlinear boundary conditions ?u/?n = g(x, u). We show that, if locally around some point of the boundary, we have f(x, u) = ?βu p , β ≥ 0, and g(x, u) = u q then, blow-up in finite time occurs if 2q > p + 1 or if 2q = p + 1 and β < q. Moreover, if we denote by T b the blow-up time, we show that a proper continuation of the blowing up solutions are pinned to the value infinity for some time interval [T, τ] with T b ≤ T < τ. On the other hand, for the case f(x, u) = ?βu p , for all x and u, with β > 0 and p > 1, we show that blow-up occurs only on the boundary. 相似文献
9.
Aregression is a functiong from a partially ordered set to itself such thatg(x)≦x for allz. Amonotone k-chain is a chain ofk elementsx
1<x
2 <...<x
k
such thatg(x
1)≦g(x
2)≦...≦g(x
k
). If a partial order has sufficiently many elements compared to the size of its largest antichain, every regression on it
will have a monotone (k + 1)-chain. Fixingw, letf(w, k) be the smallest number such that every regression on every partial order with size leastf(w, k) but no antichain larger thanw has a monotone (k + 1)-chain. We show thatf(w, k)=(w+1)
k
.
Dedicated to Paul Erdős on his seventieth birthday
Research supported in part by the National Science Foundation under ISP-80-11451. 相似文献
10.
LetT(λ) be a bounded linear operator in a Banach spaceX for eachλ in the scalar fieldS. The characteristic value-vector problemT(λ)x = 0 with a normalization conditionφ x = 1, whereφ ε X
*, is formulated as a nonlinear problem inX xS:P(y) ≡ (T(λ)x, φ x - 1) = 0,y= (X, A). Newton's method and the Kantorovič theorem are applied. For this purpose, representations and criteria for existence
ofP′(y)−1 are obtained. The continuous dependence onT of characteristic values and vectors is investigated. A numerical example withT(λ) =A +λB +λ
2
C is presented.
Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462. 相似文献
11.
Sudhasree Gadam 《Rendiconti del Circolo Matematico di Palermo》1992,41(2):209-220
We study the behaviour of the positive solutions to the Dirichlet problem IR
n
in the unit ball in IR
R
wherep<(N+2)/(N−2) ifN≥3 and λ varies over IR. For a special class of functionsg viz.,g(x)=u
0
p
(x) whereu
0 is the unique positive solution at λ=0, we prove that for certain λ’s nonradial solutions bifurcate from radially symmetric
positive solutions. WhenN=1, we obtain the complete bifurcation diagram for the positive solution curve. 相似文献
12.
Huiling Li Peter Y. H. Pang Mingxin Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,89(1):295-311
We study the existence, uniqueness, and asymptotic behavior of blow-up solutions for a general quasilinear elliptic equation
of the type −Δ
p
u = a(x)u
m
−b(x)f(u) with p > 1 and 0 < m < p−1. The main technical tool is a new comparison principle that enables us to extend arguments for semilinear equations to
quasilinear ones. Indeed, this paper is an attempt to generalize all available results for the semilinear case with p = 2 to the quasilinear case with p > 1. 相似文献
13.
Ruan Huojun Dai Meifeng Su Weiyi Dept. of Math. Zhejiang Univ. Hangzhou China. Dept. of Math. Jiangsu Univ. Zhenjiang China. Dept. of Math. Nanjing Univ. Nanjing China. 《高校应用数学学报(英文版)》2005,20(2):235-242
§ 1 IntroductionThe class of Cantor sets is a typical one of sets in fractal geometry.Mathematicianshave paid their attentions to such sets for a long time.Itis well known that the Hausdorffmeasure of the Cantor middle- third set is1(see[1]) .Recently,Feng[3] obtained the exactvalues of the packing measure for a class of linear Cantor sets.Using Feng s method,Zhuand Zhou[5] obtained the exactvalue of Hausdorff centred measure of the symmetry Cantorsets.In this papar,we consider the Ha… 相似文献
14.
Nadia J. Gal James E. Jamison Aristomenis G. Siskakis 《Complex Analysis and Operator Theory》2010,4(2):245-255
We are interested in the isometric equivalence problem for the Cesàro operator
C(f) (z) = \frac1z ò0zf(x) \frac11-xd x{C(f) (z) =\frac{1}{z} \int_{0}^{z}f(\xi) \frac{1}{1-\xi}d \xi} and an operator
Tg(f)(z)=\frac1zò0zf(x) g¢(x) d x{T_{g}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\xi) g^{\prime}(\xi) d \xi}, where g is an analytic function on the disc, on the Hardy and Bergman spaces. Then we generalize this to the isometric equivalence
problem of two operators Tg1{T_{g_{1}}} and Tg2{T_{g_{2}}} on the Hardy space and Bergman space. We show that the operators Tg1{T_{g_{1}}} and Tg2{T_{g_{2}}} satisfy Tg1U1=U2Tg2{T_{g_{1}}U_{1}=U_{2}T_{g_{2}}} on H
p
, 1 ≤ p < ∞, p ≠ 2 if and only if g2(z) = lg1(eiqz){g_{2}(z) =\lambda g_{1}(e^{i\theta}z) }, where λ is a modulus one constant and U
i
, i = 1, 2 are surjective isometries of the Hardy Space. This is analogous to the Campbell-Wright result on isometrically equivalence
of composition operators on the Hardy space. 相似文献
15.
Shu-Yu Hsu 《Mathematische Annalen》2003,325(4):665-693
We prove that the solution u of the equation u
t
=Δlog u, u>0, in (Ω\{x
0})×(0,T), Ω⊂ℝ2, has removable singularities at {x
0}×(0,T) if and only if for any 0<α<1, 0<a<b<T, there exist constants ρ0, C
1, C
2>0, such that C
1
|x−x
0|α≤u(x,t)≤C
2|x−x
0|−α holds for all 0<|x−x
0|≤ρ0 and a≤t≤b. As a consequence we obtain a sufficient condition for removable singularities at {∞}×(0,T) for solutions of the above equation in ℝ2×(0,T) and we prove the existence of infinitely many finite mass solutions for the equation in ℝ2×(0,T) when 0≤u
0∉L
1
(ℝ2) is radially symmetric and u
0L
loc
1(ℝ2).
Received: 16 December 2001 / Revised version: 20 May 2002 / Published online: 10 February 2003
Mathematics Subject Classification (1991): 35B40, 35B25, 35K55, 35K65 相似文献
16.
Ravi P. Agarwal Donal O'Regan 《Journal of Mathematical Analysis and Applications》2003,279(2):597-616
We consider the singular boundary value problem for the differential equation x″+f(t,x,x′)=0 with the boundary conditions x(0)=0, w(x(T),x′(T))+?(x)=0. Here f is a Carathéodory function on which may by singular at the value x=0 of the phase variable x and f may change sign, w is a continuous function, and ? is a continuous nondecreasing functional on C0([0,T]). The existence of positive solutions on (0,T] in the classes AC1([0,T]) and C0([0,T])∩AC1loc((0,T]) is considered. Existence results are proved by combining the method of lower and upper functions with Leray-Schauder degree theory. 相似文献
17.
Norbert Steinmetz 《Israel Journal of Mathematics》2002,128(1):29-52
We consider the solutions of the First Painlevé Differential Equationω″=z+6w
2, commonly known as First Painlevé Transcendents. Our main results are the sharp order estimate λ(w)≤5/2, actually an equality, and sharp estimates for the spherical derivatives ofw andf(z)=z
−1
w(z
2), respectively:w#(z)=O(|z|3/4) andf#(z)=O(|z|3/2). We also determine in some detail the local asymptotic distribution of poles, zeros anda-points. The methods also apply to Painlevé’s Equations II and IV. 相似文献
18.
Antonio Tineo 《Annali di Matematica Pura ed Applicata》2003,182(2):129-141
In this paper we study the scalar equation x′=f(t,x), where f(t,x) has cubic non-linearities in x and we prove that this equation has at most three bounded separate solutions. We say that λ∈ℝ is a critical value of the
equation x′=f(t,x)+λx if this equation has a degenerate bounded solution and we exhibit two classes of functions f such that the above equation has a unique critical value.
Received: February 4, 2000; in final form: March 19, 2002?Published online: April 14, 2003
RID="*"
ID="*"This paper was partially supported by CDCHT, Universidad de los Andes. 相似文献
19.
Antonio Tineo 《Annali di Matematica Pura ed Applicata》2003,182(2):113-128
In this paper, we prove a result of Ambrosetti–Prodi type for the problem x′=f(t,x)+λx, where f(t,x) is T-periodic in t, f(t,0)≡0 and f(t,x) has “cubic nonlinearities”.
Received: February 4, 2000?Published online: April 14, 2003
RID="*"
ID="*"This paper was partially supported by CDCHT, Universidad de los Andes. 相似文献
20.
Yujuan Chen Mingxin Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,103(1):277-292
Under the proper structure conditions on the nonlinear term f(u) and weight function b(x), the paper shows the uniqueness and asymptotic behavior near the boundary of boundary blow-up solutions to the porous media
equations of logistic type −Δu = a(x)u
1/m
− b(x)f(u) with m > 1. 相似文献